This study will compare giving a new drug called 3TC (lamivudine) and ZDV (zidovudine) together to giving DDI (Didanosine) alone or DDI and ZDV together. The use of 3TC and ZDV together has been tested in adults and children in other studies and has been found safe to use. The 3TC and ZDV together reduced how much HIV was in the patient's blood and increased the number of white blood cells that help the immune system fight infection. The purpose is to see which one of the treatments does the best job of slowing down the HIV disease in children.